Question 63545
<b>
{{{(1+cot^2x)(1-cos2x) = 2}}}</b>

There are two identities you need to solve this:

(1) sin^2x+cos^2x=1
(2) cos2x=1-2sin^2x

Remember that cotx = 1/tanx = 1/(sinx/cosx) = cosx/sinx.

Then, 1+cot^2x = 1+(cos^2x/sin^2x).
Turn 1 into cos^2x/cos^2x then 1+(cos^2x/sin^2x) becomes (cos^2x+sin^2x)/sin^2x = 1/sin^2x.

So, 1+cot^2x = 1/sin^2x.

Now, 1-cos2x = 1-(1-2sin^2x) = 2sin^2x.

So, (1+cot^2x)(1-cos2x) = (1/sin^2x)(2sin^2x) = 2 which is what we were trying to prove.

Make sense?